lib/Analysis/LoopAnalysis.cpp

//===- LoopAnalysis.cpp - Misc loop analysis routines //-------------------===//
//
// Copyright 2019 The MLIR Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//   http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// =============================================================================
//
// This file implements miscellaneous loop analysis routines.
//
//===----------------------------------------------------------------------===//

#include "mlir/Analysis/LoopAnalysis.h"

#include "mlir/Analysis/AffineAnalysis.h"
#include "mlir/Analysis/AffineStructures.h"
#include "mlir/Analysis/MLFunctionMatcher.h"
#include "mlir/IR/Builders.h"
#include "mlir/IR/BuiltinOps.h"
#include "mlir/IR/Statements.h"
#include "mlir/StandardOps/StandardOps.h"
#include "mlir/Support/Functional.h"
#include "mlir/Support/MathExtras.h"

using namespace mlir;

/// Returns the trip count of the loop as an affine expression if the latter is
/// expressible as an affine expression, and nullptr otherwise. The trip count
/// expression is simplified before returning.
AffineExpr mlir::getTripCountExpr(const ForStmt &forStmt) {
  // upper_bound - lower_bound + 1
  int64_t loopSpan;

  int64_t step = forStmt.getStep();
  auto *context = forStmt.getContext();

  if (forStmt.hasConstantBounds()) {
    int64_t lb = forStmt.getConstantLowerBound();
    int64_t ub = forStmt.getConstantUpperBound();
    loopSpan = ub - lb + 1;
  } else {
    auto lbMap = forStmt.getLowerBoundMap();
    auto ubMap = forStmt.getUpperBoundMap();
    // TODO(bondhugula): handle max/min of multiple expressions.
    if (lbMap.getNumResults() != 1 || ubMap.getNumResults() != 1)
      return nullptr;

    // TODO(bondhugula): handle bounds with different operands.
    // Bounds have different operands, unhandled for now.
    if (!forStmt.matchingBoundOperandList())
      return nullptr;

    // ub_expr - lb_expr + 1
    AffineExpr lbExpr(lbMap.getResult(0));
    AffineExpr ubExpr(ubMap.getResult(0));
    auto loopSpanExpr = simplifyAffineExpr(
        ubExpr - lbExpr + 1, std::max(lbMap.getNumDims(), ubMap.getNumDims()),
        std::max(lbMap.getNumSymbols(), ubMap.getNumSymbols()));
    auto cExpr = loopSpanExpr.dyn_cast<AffineConstantExpr>();
    if (!cExpr)
      return loopSpanExpr.ceilDiv(step);
    loopSpan = cExpr.getValue();
  }

  // 0 iteration loops.
  if (loopSpan < 0)
    return 0;

  return getAffineConstantExpr(static_cast<uint64_t>(ceilDiv(loopSpan, step)),
                               context);
}

/// Returns the trip count of the loop if it's a constant, None otherwise. This
/// method uses affine expression analysis (in turn using getTripCount) and is
/// able to determine constant trip count in non-trivial cases.
llvm::Optional<uint64_t> mlir::getConstantTripCount(const ForStmt &forStmt) {
  auto tripCountExpr = getTripCountExpr(forStmt);

  if (!tripCountExpr)
    return None;

  if (auto constExpr = tripCountExpr.dyn_cast<AffineConstantExpr>())
    return constExpr.getValue();

  return None;
}

/// Returns the greatest known integral divisor of the trip count. Affine
/// expression analysis is used (indirectly through getTripCount), and
/// this method is thus able to determine non-trivial divisors.
uint64_t mlir::getLargestDivisorOfTripCount(const ForStmt &forStmt) {
  auto tripCountExpr = getTripCountExpr(forStmt);

  if (!tripCountExpr)
    return 1;

  if (auto constExpr = tripCountExpr.dyn_cast<AffineConstantExpr>()) {
    uint64_t tripCount = constExpr.getValue();

    // 0 iteration loops (greatest divisor is 2^64 - 1).
    if (tripCount == 0)
      return ULONG_MAX;

    // The greatest divisor is the trip count.
    return tripCount;
  }

  // Trip count is not a known constant; return its largest known divisor.
  return tripCountExpr.getLargestKnownDivisor();
}

bool mlir::isAccessInvariant(const MLValue &input, MemRefType memRefType,
                             ArrayRef<MLValue *> indices, unsigned dim) {
  assert(indices.size() == memRefType.getRank());
  assert(dim < indices.size());
  auto layoutMap = memRefType.getAffineMaps();
  assert(memRefType.getAffineMaps().size() <= 1);
  // TODO(ntv): remove dependency on Builder once we support non-identity
  // layout map.
  Builder b(memRefType.getContext());
  assert(layoutMap.empty() ||
         layoutMap[0] == b.getMultiDimIdentityMap(indices.size()));
  (void)layoutMap;

  SmallVector<OperationStmt *, 4> affineApplyOps;
  getReachableAffineApplyOps({indices[dim]}, affineApplyOps);

  if (affineApplyOps.empty()) {
    // Pointer equality test because of MLValue pointer semantics.
    return indices[dim] != &input;
  }

  assert(affineApplyOps.size() == 1 &&
         "CompositionAffineMapsPass must have "
         "been run: there should be at most one AffineApplyOp");
  auto composeOp = affineApplyOps[0]->cast<AffineApplyOp>();
  // We need yet another level of indirection because the `dim` index of the
  // access may not correspond to the `dim` index of composeOp.
  unsigned idx = std::numeric_limits<unsigned>::max();
  unsigned numResults = composeOp->getNumResults();
  for (unsigned i = 0; i < numResults; ++i) {
    if (indices[dim] == composeOp->getResult(i)) {
      idx = i;
      break;
    }
  }
  assert(idx < std::numeric_limits<unsigned>::max());
  return !AffineValueMap(*composeOp)
              .isFunctionOf(idx, &const_cast<MLValue &>(input));
}

/// Determines whether a load or a store has a contiguous access along the
/// value `input`. Contiguous is defined as either invariant or varying only
/// along the fastest varying memory dimension.
// TODO(ntv): allow more advanced notions of contiguity (non-fastest varying,
// check strides, ...).
template <typename LoadOrStoreOpPointer>
static bool isContiguousAccess(const MLValue &input,
                               LoadOrStoreOpPointer memoryOp,
                               unsigned fastestVaryingDim) {
  using namespace functional;
  auto indices = map([](SSAValue *val) { return dyn_cast<MLValue>(val); },
                     memoryOp->getIndices());
  auto memRefType = memoryOp->getMemRefType();
  for (unsigned d = 0, numIndices = indices.size(); d < numIndices; ++d) {
    if (fastestVaryingDim == (numIndices - 1) - d) {
      continue;
    }
    if (!isAccessInvariant(input, memRefType, indices, d)) {
      return false;
    }
  }
  return true;
}

template <typename LoadOrStoreOpPointer>
static bool isVectorElement(LoadOrStoreOpPointer memoryOp) {
  auto memRefType = memoryOp->getMemRefType();
  return memRefType.getElementType().template isa<VectorType>();
}

bool mlir::isVectorizableLoop(const ForStmt &loop, unsigned fastestVaryingDim) {
  if (!matcher::isParallelLoop(loop) && !matcher::isReductionLoop(loop)) {
    return false;
  }

  // No vectorization across conditionals for now.
  auto conditionals = matcher::If();
  auto *forStmt = const_cast<ForStmt *>(&loop);
  auto conditionalsMatched = conditionals.match(forStmt);
  if (!conditionalsMatched.empty()) {
    return false;
  }

  auto loadAndStores = matcher::Op(matcher::isLoadOrStore);
  auto loadAndStoresMatched = loadAndStores.match(forStmt);
  for (auto ls : loadAndStoresMatched) {
    auto *op = cast<OperationStmt>(ls.first);
    auto load = op->dyn_cast<LoadOp>();
    auto store = op->dyn_cast<StoreOp>();
    // Only scalar types are considered vectorizable, all load/store must be
    // vectorizable for a loop to qualify as vectorizable.
    // TODO(ntv): ponder whether we want to be more general here.
    bool vector = load ? isVectorElement(load) : isVectorElement(store);
    if (vector) {
      return false;
    }
    bool contiguous = load ? isContiguousAccess(loop, load, fastestVaryingDim)
                           : isContiguousAccess(loop, store, fastestVaryingDim);
    if (!contiguous) {
      return false;
    }
  }
  return true;
}

/// Checks whether SSA dominance would be violated if a for stmt's body
/// statements are shifted by the specified shifts. This method checks if a
/// 'def' and all its uses have the same shift factor.
// TODO(mlir-team): extend this to check for memory-based dependence
// violation when we have the support.
bool mlir::isStmtwiseShiftValid(const ForStmt &forStmt,
                                ArrayRef<uint64_t> shifts) {
  assert(shifts.size() == forStmt.getStatements().size());
  unsigned s = 0;
  for (const auto &stmt : forStmt) {
    // A for or if stmt does not produce any def/results (that are used
    // outside).
    if (const auto *opStmt = dyn_cast<OperationStmt>(&stmt)) {
      for (unsigned i = 0, e = opStmt->getNumResults(); i < e; ++i) {
        const MLValue *result = opStmt->getResult(i);
        for (const StmtOperand &use : result->getUses()) {
          // If an ancestor statement doesn't lie in the block of forStmt, there
          // is no shift to check.
          // This is a naive way. If performance becomes an issue, a map can
          // be used to store 'shifts' - to look up the shift for a statement in
          // constant time.
          if (auto *ancStmt = forStmt.findAncestorStmtInBlock(*use.getOwner()))
            if (shifts[s] != shifts[forStmt.findStmtPosInBlock(*ancStmt)])
              return false;
        }
      }
    }
    s++;
  }
  return true;
}